Casting
DPS
increase by Cooldown Reduction

1 - Old CDR
1 - New CDR

Example:
If you have 0% CDR and you get 40% CDR

1 - 0
1 - 0.40

= 1.66666
Therefore, your casting DPS goes up by 66.66% with 40% CDR.

Concept:
You can confirm the above example with this very simple logic.
Say there is a spell with 10s cooldown. In 60 seconds, you
can cast it 6 times.
Now with 40% cooldown reduction, the new cooldown of the spell becomes
6s which means you can cast it 10 times in 60 seconds.
Hence, the casting DPS is 10/6 = 1.6666

%
Increase in
Durability by Armor Against Only Physical Damage

100
+ New Armor100 + Old Armor

Example:
If you have 50 armor and you purchase (100 armor), you now
have 150 armor.

100 + 150
100 + 50

= 1.66666

Therefore, you are now 1.6666 times more durable against physical
attacks (66.7% tankier
against physical attacks)
Or take the reciprocal of that (1/answer) and you are left with 0.60
which means you take 40%
less damage relative to when you didn't have

Concept
You can confirm the above example with this very simple logic.
When an enemy champion with 100 Attack Damage autoattacks you,

With 50 armor,
you take 66.66 damage
With 150 armor,
you take 40 damage

%
Increase in
DPS by Critical Strike

Example:
When you have 0% critical chance, the critical strike and damage
portion of will increase your DPS
by,

1 + 0.20 * (1.5)
1 + 0 * (1)

= 1.3
Therefore, your DPS has increased by 30% relative to before with only
the critical strike stat portion of Concept:
You can confirm the above example with this very simple logic.
When you auto-attack 5 times, you deal

= 1.328
Therefore, you are now 32.8% tankier with
for the above conditions(or take the
reciprocal of that which is 0.753 so you take
24.7% less damage relative to before)Concept: Given the damage
type you can reduce the amount with armor, magic
resist, and attack speed slow when applicable.Then you can
compare the difference of the actual damage you receive.